How to make fullscreen app's space appear next to the current space?
Normally it goes to the end of the list of spaces.
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while pressing the alt key will put it right next to the current desktop, at least on Mavericks.
I assume you mean that, when you make an app window enter fullscreen mode, you want that window to appear next to the current Space (by default it appears at the end of the Spaces list, as you say).
On macOS 11 Big Sur (and possibly older versions), you can do this as follows:
(If you mean, how do you move an existing fullscreen app so it's next to another space, then just go into Mission Control and drag the app's thumbnail in the row of Spaces at the top.)